Re: Can you suggest six names of great mathematicians quickly?

Dear BobbyM,May I know from where are you getting all these facts?Dear anonimnystefy,The other two which we have chosen are Pythagoras and Turing.BTW Is Turing OK?..Some of my classmates don't keep track of Mathematics so I need your advice?

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.''God exists because Mathematics is consistent, and the devil exists because we cannot prove it''But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

Re: Can you suggest six names of great mathematicians quickly?

HiI like stories very much?What has Turing contributed to Mathematics

Last edited by Agnishom (2012-06-15 20:34:24)

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.''God exists because Mathematics is consistent, and the devil exists because we cannot prove it''But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

Re: Can you suggest six names of great mathematicians quickly?

Does it mean you were making it up?If so, you have awesome creativity

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.''God exists because Mathematics is consistent, and the devil exists because we cannot prove it''But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

Re: Can you suggest six names of great mathematicians quickly?

The wikipedia says that the Fibonacci Sequence is a complete sequence which means any integer can be expressed as a sum of fibonacci numbers.

Can you so how it is proved?

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.''God exists because Mathematics is consistent, and the devil exists because we cannot prove it''But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

Re: Can you suggest six names of great mathematicians quickly?

Would you show it here please?What is this induction thing?

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.''God exists because Mathematics is consistent, and the devil exists because we cannot prove it''But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

Re: Can you suggest six names of great mathematicians quickly?

Bob,What you said in post #38 shows the algorithm to find the representation. But how can you prove that that algorithm will always be possible for any number?

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.''God exists because Mathematics is consistent, and the devil exists because we cannot prove it''But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

Re: Can you suggest six names of great mathematicians quickly?

Hmmm....Its 9:02 PM in our countryFeeling Sleepy!

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.''God exists because Mathematics is consistent, and the devil exists because we cannot prove it''But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

Re: Can you suggest six names of great mathematicians quickly?

hi Agnishom,

Night night then.

Here's the proof for when you wake.

Let's call the number N.

If N is a Fibonacci number then there's nothing to do, because you either accept that a 'sum' can have just one number or if that makes you unhappy, you write it as the sum of the two Fibonacci numbers that made it by definition.

So what if it isn't?

The algorithm requires that we find the next F number below N and subtract it.

Can we definitely do this and be sure we never repeat an F ?

Let the next Fibonacci number above N, be (a + b) where a and b are the two F numbers that made it. The Fs go on for ever so there will certainly be one that is just bigger than N.

Suppose also that a < b.

Then b is the next F number going down from N. ie. b < N < a + b

For if there was another F number squeezing between b and N, let's call it 'c', then b + c is the next F number after N, not a + b.

The algorithm requires that we compute N - b and write b in the list. (You always subtract the biggest F that you can.)

So we are left with a remainder of N-b

Now N < a + b => N - b < a.

So if we now replace N with N - b in the algorithm we will never be able to subtract b again because N - b < a < b

So b will only occur in the list once.

So on this next loop our (new N) is now the (old N) - b

So can we carry on finding smaller and smaller Fs to subtract.

Yes, because 1, 2 and 3 are F numbers so we can either find a bigger F between 3 and N or we must be looking at N = 1, 2 or 3.

So eventually we must escape from the loop.

This is essentially the proof in the Wiki article. I've just put it into words that, hopefully, make it easier to understand.

I found it was best to try some examples.

eg 1) N = 67 b = 55 new N = 67 - 55 = 12.

N = 12 this isn't an F so b = 8 new N = 12 - 8 = 4

N = 4 this isn't an F so b = 3 new N = 4 - 3 = 1

N = 1 this is an F so stop.

67 = 55 + 8 + 3 + 1

eg 2) N = 103 b = 89 new N = 103 - 89 = 14

N = 14 b = 13 new N = 14 - 13 = 1

103 = 89 + 14 + 1

Try it yourself and you'll find it always works.

Bob

Children are not defined by school ...........The FonzYou cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

Re: Can you suggest six names of great mathematicians quickly?

Hi Bob

I have a problem with your first line:

bob bundy wrote:

or if that makes you unhappy, you write it as the sum of the two Fibonacci numbers that made it by definition.

The theorem states that you can write any number as a sum of non-adjacent Fibonacci numbers not including F[1] , which means that a Fibonacci number must be written as a sum of only one element - itself, as you stated in the first part of the sentence.

Here lies the reader who will never open this book. He is forever dead.Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and PunishmentThe knowledge of some things as a function of age is a delta function.

Re: Can you suggest six names of great mathematicians quickly?

Here lies the reader who will never open this book. He is forever dead.Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and PunishmentThe knowledge of some things as a function of age is a delta function.

Re: Can you suggest six names of great mathematicians quickly?

I have seen it. It is worth it to try posting it again.

Here lies the reader who will never open this book. He is forever dead.Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and PunishmentThe knowledge of some things as a function of age is a delta function.